A note on Poisson stability and controllability

The connection between Poisson stability and controllability is revisited. For the controllability criterion based on weakly positive Poisson stability (WPPS) and Lie algebra rank condition (LARC), it is shown that two natural assumptions about the set of input values are necessary for strictness. By using the relationship between conservative property and WPPS, sufficient conditions for controllability of affine nonlinear systems are further discussed. At last, for systems defined on compact Riemannian manifold, the WPPS is proved to be equivalent to Poisson stability.     

A note on the stability of elastico-viscous liquids

Summary The stability criterion for an elastico-viscous liquid in Couette flow is compared with that for a non-Newtonian liquid exhibiting the same variation in apparent viscosity. It is shown that the presence of elasticity has a destabilizing effect on the flow.     

A note on the stability of Beltrami fields for compressible fluid flows

In this paper we study the stability of the magnetostatic equilibrium through a relaxation of a magnetic field B in perfectly conducting compressible and viscous fluid.We establish stability criterion of a large class of Beltrami flows to any admissible displacement about the equilibrium configuration. We show that the field is stable to any displacement with the same 2π-periodicity as the basic flow, except the case where perturbations with wavelength much greater than the scale of the basic flow are included.     

A note on the stability and accuracy of Cn finite elements in steady diffusion-convection problems

The paper is concerned with stability and accuracy of an nth order Lagrangian family of finite element steady-state solutions of the diffusion-convection equation, and furthermore is concerned with the stability and the accuracy of on mth kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pe_c ( = uh/k). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pe_c for P^1,3, and for P^2,5 the stable solution is obtained for Pe_c less than 44.4.     

A note on the stability of solutions of the Hill equation with a square-wave coefficient

The results of Van der Pol and Strutt [Phil. Mag.5, 18 (1928)] on the stability of solutions to the Hill equation for a square-wave coefficient have been re-examined. More accurate and extensive results for the stability boundaries are presented, with emphasis on the closed unstable regions which are imbedded in the stable regions.     

A note on the implications of thermodynamic stability in the internal variable theory of inelastic solids

Recently developed internal theories for inelastic solids are considered, and the consequences of thermodynamic stability requirements are explored. The results are expressed in a form which permits comparison with the stability postulates of Drucker and Ilyushin.     

A note on estimating mastercurves

There are several quantities in theology which show a scaling behavior. One well known example is the time-temperature superposition principle of material functions characterizing the linear viscoelastic properties of polymer melts. We propose a mathematical shift procedure for the calculation of mastercurves and the corresponding scaling factors from experimental data which show such a scaling behavior. In order to demonstrate the applicability of the shift procedure mastercurves and scaling factors are determined for material functions of several polystyrene melts and for the specific viscosity of polyisobutylene in cyclohexane.     

A note on planar kineto-elasto-dynamics

Summary Dynamic analyses of flexible linkages are generally performed by considering small displacements from a predefined reference configuration. A reference mechanism is commonly defined for this purpose. The definition of a reference mechanism is subjected to some restricting conditions which are analyzed here for planar articulated linkages. A second part of this note documents a simplified form of the equations of motion for flexible planar mechanisms. The virtual displacement is approximated in the same way as accelerations, when secondary terms are neglected. A comparison between experimental findings and results of numerical integrations shows that, in the present case-study, the introduced approximation only corresponds to a light stiffening of the mathematical model.

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Sommario L'analisi dinamica di meccanismi flessibili viene generalmente eseguita nell'ipotesi di piccoli spostamenti da una configurazione di riferimento. A questo scopo si definisce comunemente un meccanismo di riferimento composto da membri rigidi. La definizione di tale meccanismo é soggetta ad alcune condizioni restrittive che vengono qui analizzate nel caso di meccanismi articolati piani. La seconda parte di questa nota illustra una forma semplificata di equazioni del moto per meccanismi piani a membri flessibili. Lo spostamento virtuale é approssimato con lo stesso criterio con il quale si approssimano le accelerazioni nel caso che si trascurino i termini secondari. Un paragone tra dati sperimentali e risultati numerici evidenzia come, nel caso in esame, le approssimazioni introdotte corrispondano solamente ad un leggero irrigidimento del modello matematico.

     

A note on non linear stability of the Poiseuille flows in anisotropic M.H.D.

Summary We study the non linear stability of the Poiseuille flows in anisotropic M.H.D. and we give a sufficient condition of exponential asymptotic stability with respect to laminar onedimensional perturbations.

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Sommario Si studia la stabilità non lineare in media dei moti di Poiseuille in M.H.D. anisotropa e si assegna una condizione sufficiente di stabilità asintotica esponenziale.

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Work performed under the auspices of the G.N.F.M.-C.N.R. and with the grant 40%-M.P.I. (Italy).